Question

Flat Stars. Consider a star in a two-dimensional universe. Suppose
that the
gravitational force law is F = (GM1M2/r).
a) Derive the continuity equation in terms of the mass per unit
area, s.
b) Derive the hydrostatic equilibrium equation. Let the pressure P
be the thermal
force per unit circumference.
c) Derive the Lane-Emden equation in this case, assuming P =
Ks?.
d) Assuming the polytropic equation and the radiative diffusion
equation apply, and
also assuming a Kramer�s opacity law (? = constant), what is the
mass-luminosity
scaling law? (Just get the scaling, don�t worry about constants.)